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Machine Learning Techniques as Alternative to Physical Models for Parametric Sweeps

Sourajeet Roy Associate Professor Computational Modeling and Simulation (CMAS) Laboratory Department of Electronics and Communication Engineering Indian Institute of Technology Roorkee

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Evolution of FET Devices

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How does TCAD execute device simulations?

Governing PDEs

Poisson Equation

Continuity Equation

Schrodinger’s Equation

Fourier Heat Diffusion Equation

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Challenges of TCAD Solvers

Substitute:

Artificial Neural Network based Surrogate Models

Coarse Mesh

Finer Mesh

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Existing ANN Methodologies and their disadvantages

Input Features (Device Parameters: L_g, T_ox)

Output Features: I_d, Q_g, Q_d…

Loss Function:

Highly Data Dependent

Huge Training Data Generation Cost

Extensive TCAD Simulations

Physical Consistency not guaranteed

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Proposed Approach: Physics Informed NNs

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Physics Informed NNs: Parametric Analysis

N_t: No. of time samples,

N_space: No. of space points,

N_p: No. of parametric points

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Physics Informed NNs: Exemption from Data Generation Cost

automatic

differentiation

No Data Generation Required !!

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Physics Informed NNs: Extrapolating Capacity

Data-driven ANN Techniques perform well in this region

But, fail to perform for values outside this range

PINNs can extrapolate beyond Training Range

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Physics Informed NNs: Physically Feasible Solutions

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Physics Informed NNs: Summarized Advantages

Highly Efficient Training

Accurate Solutions

Physically Consistent Solutions

Extrapolative beyond training range

Physics Informed Machine Learning

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Proof of Concept: PINNs applied on a Multiconductor Transmission Line Setup

Comparison between Data-Driven ANN and PINNs

Training Methodology	Total Training Time	Memory
Data-Driven ANNs	2686.51 min (Data Generation) + 305.42 min (Optimization Time)	1505.26 KB
PINNs	311.66 min (Optimization Time)	684.21 KB

Telegrapher’s Partial Differential eqⁿ :

MNA eqⁿ :

Initial condition eqⁿ :

v and i are the node voltages and branch currents for all time points and parametric points

Comparison of Training Efficiency and Memory Efficiency between PINN and Data-driven ANN technique

>9 times training efficient

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Related Published Works

A. Verma, D. Basu, A. Dasgupta and S. Roy, "Efficient Stochastic Modeling of Distributed Transmission Line Networks using Homotopy Assisted Physics Informed Neural Networks", IEEE Workshop on Signal and Power Integrity (SPI), Turin, Italy, June 2026.

2. D. Basu, A. Verma, A. Dasgupta and S. Roy, "MINNs: MNA Informed Neural Networks for Fast

Transient Simulation of Nonlinear Transmission Lines Subject to Parametric Uncertainty", IEEE

Transactions on Components, Packaging and Manufacturing Technology, 2026.

3. D. Basu, A. Verma, A. Dasgupta and S. Roy, "MINNs: MNA Informed Neural Networks for Efficient

Uncertainty Quantification of Nonlinear Transmission Lines", Asia Pacific Microwave Conference

(APMC), Jeju, Korea, 2025.